Joseph Smith, in his editing for the 1837 edition, inserted the subordinate conjunction that into this passage, perhaps in an attempt to link the resulting subordinate clause to the two that-clauses earlier in this verse:
Yet the immediately following text in this same verse shows that the repetition of the that is not necessary:
Moreover, we are not required to interpret “the light of everlasting life was lit up in his soul” as a subordinate clause. Instead, this final clause can be interpreted as providing another way of referring to the change that had overcome king Lamoni. In other words, we basically have a sequence of two main clauses, with a present participial clause intervening between those two clauses (and separated off by dashes in the following):
In this instance, the original text works well enough and does not need to be emended by adding an additional that.
Another possibility is that Joseph’s extra that was an attempt to provide a resultive clause for the preceding occurrence of such. Yet if this were so, the and should have been deleted:
Although the original manuscript is not extant for this precise part of the text, spacing between extant fragments argues that there was no room in 𝓞 for a that except by supralinear insertion. The critical text will therefore restore the original phraseology in Alma 19:6—that is, without any that after the and: “and the light of everlasting life was lit up in his soul”.
Summary: Remove in Alma 19:6 the unnecessary that introduced by Joseph Smith after the and that precedes the clause “the light of everlasting life was lit up in his soul”.